Economics 528 In che HKUST Spring 2004 Review Problems for Midterm 1 Least Squares 1. In the linear regression model y=XB+E there is a need for changing the unit of measurement for the dependent variable y So y*= cy(c is a constant)is now used as a dependent variable (a) Does this practice change R2? (b)What happens to R if the unit of measurement is changed only for the regressor? 2. Consider the linear regression model =Q+x+=,~td(2),≠0 (a) Is the Ols estimator of B affected by the nonzero mean of Ei? (b)Can the least squares estimator of a estimate it accurately? 3. Prove that the OlS estimators of B, in the following linear models are identical 1+t2 B1+ where yt and at are de-trended yt and at obtained by regressing gt and t on t and setting 3 and at equal to the respective residuals 4. Discuss the validity of the following stat ements (a) Sum of residuals is always zero (b)If a regression produces R greater than 0.5, the regression is a reliable oneEconomics 528 HKUST In Choi Spring 2004 Review Problems for Midterm 1 Least Squares 1. In the linear regression model y = Xβ + ε, there is a need for changing the unit of measurement for the dependent variable y. So y ∗ = cy (c is a constant) is now used as a dependent variable. (a) Does this practice change R2 ? (b) What happens to R2 if the unit of measurement is changed only for the regressor? 2. Consider the linear regression model yi = α + β ′Xi + εi , εi ∼ iid
µ, σ2 , µ = 0 (a) Is the OLS estimator of β affected by the nonzero mean of εi? (b) Can the least squares estimator of α estimate it accurately? 3. Prove that the OLS estimators of β1 in the following linear models are identical yt = xtβ1 + tβ2 + εt y ∗ t = x ∗ tβ1 + εt where y ∗ t and x ∗ t are de—trended yt and xt obtained by regressing yt and xt on t and setting y ∗ t and x ∗ t equal to the respective residuals. 4. Discuss the validity of the following statements. (a) Sum of residuals is always zero. (b) If a regression produces R2 greater than 0.5, the regression is a reliable one.